Rotation matrix

1. The problem statement, all variables and given/known data

A have two points

60,892857 12,496875 -4,837500

70,714286 14,915625 -5,240625

I have to rotate for -0,067195795 radians.







2. Relevant equations



##\begin{bmatrix}

{x}'\\

{y}'

\end{bmatrix}=\begin{bmatrix}

cos\alpha & -sin\alpha \\

sin\alpha & cos\alpha

\end{bmatrix}\begin{bmatrix}

x\\

y

\end{bmatrix}##



3. The attempt at a solution



Just to explain my data:

60,892857 12,496875 -4,837500

70,714286 14,915625 -5,240625



The first column is x value, the second one is y and the third one is also y. So the idea is, that these points represent some kind of a body, and the problem says I have to rotate for given angle and plot both bodies; rotated and original.



My problem here is very basic and it may sound stupid but:



After calculating the new x and y value using the rotation matrix for first and second column I get

61,59454052 8,380006791

71,55621175 10,13383602



BUT calculating the new x and y value for the first and third column gives me

60,43061978 -8,915248198

70,20281554 -9,976925593



HOW ON EARTH IS THAT POSSIBLE?



Both y values were at the same x before rotation, and they should also be after the rotation. So my question to you is, why the hell aren't they?